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X MM Y WLL (HOLLPWAWL i? and 0M3 }‘€ 10:0 SUNS HEIGHT IN INCHES Scatter diagram for the heights of 1078 fathers and their sons, based on Pearson‘s data. There is a positive association between the heights
of the fathers and sons. The dots in the vertical strip over 72"
represent all the father—son pairs where the father is 6' tall, to the
nearest'inch. .The average height of the corresponding sons is about 71".
Similarly, the average heights of the sons of the 6A" fathers is about
67“. An 8" increase in fathers' heights (from 6M" to 72") is associated
with a 4" increase in sons‘ heights, on the average. Each oneinch in
crease in fathers' heights is associated with a half—inch increase in
their sons‘ heights, on the average. The association is bound to be
fairly weak, because there is so much variability in the heights of the
sons even after fixing their father‘s height. For instance, the sons of
the 6‘ fathers show almost as much variability in height as do all the sons together. 60 62 61 66 66 7D 72 71 76 78 FRTHERS HEIGHT IN INCHES 80 THE CORRELATION COEFFICIENT The correlation coefﬁcient—six positive values. The dia
grams are scaled so that the average equals 3 and the SD equals 1, hori
zontally and vertically; there are 50 points in each diagram. Clustering is
measured by the correlation coefﬁcient. CORR COEFF IS 0.00 CORR COEFF IS 0.40
6  6 _,
5 — 5 1
4 — 4 1
c ’ l
3  3 1 '
2 — 2 1
1 — 1 1
O 1 r l I I l '1 O 1—‘*"1——r——r———r———~r%
o 1 2 3 4 5 6 o 1 2 3 4 5 6
CORR COEFF IS 0.60 CORR COEFF Is 0.80
6  6 _
5 l 5 
41 4 J
I
'
3 ‘1 . 3 J
2 1 2 1 "
1  3 1 _
0 1—" I I I" I 'T" I O T—‘ﬁr—I——T"’—"—l—r—_}
o 1 2 3 4 5 6 o 1 2 3 4 5 6
CORR COEFF IS 0.90 CORR COEFF Is 0.95
6 6
l l
5 1 5 —
4 — 4 
3 sl .
2  1  2 1  ’
11 . 11 ,
0‘] ”"T—"“ 'l l' —l l '—I 0 4*—r——r—I——'—1—r——1
o 1 2 3 4 5 6 o 1 2 3 4 5 6 U1 4:. CO The correlation coefﬁcient—six negative values. The dia
grams are scaled so the average equals 3 and the SD equals 1, horizontally
and vertically; there are 50 points in each diagram. Clustering is measured
by the correlation coefﬁcient. CORR COEFF IS 0.30 CORR COEFF IS O.50 ﬂ 6 —
—I 5 1
J 4 J
 3 J . o
I I
_ 2 _
_. 1 ._ 1 I I I I I l O ‘I I l I ‘l‘ 1
0 1 2 3 4 5 6 O 1 2 3 4 6
CORR COEFF IS —0.7O CORR COEFF IS —O.90 6 _
I .
I 5 I
o . I o
I . . 44 .. . 
I . _ 3] ‘.‘
I ' . ' 2J ' . 1
I 1 I . ’l _l‘_ I"  r—— I I OJ l 7—. I 'T‘" "I
0 1 2 3 4 5 6 0 1 2 4 6
CORR COEFF IS O.95 CORR COEFF IS 0.99 Bl
51 .
. 4  3.“ .0
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 Spring '08
 AlexeiStepanov
 Statistics, Probability

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